acorridor is lighted by 4 lamps s10cm apart and suspended at a height of 5m above the centre of the floor. if each lamp gives 200cp in all directions below the horinzontal, find the illumination at the point on the floor mid-way between the second and third lamps
To find the illumination at the point on the floor mid-way between the second and third lamps, we can consider the contributions of each individual lamp and then sum them up.
Given:
- The lamps are 10 cm (0.1 m) apart.
- The lamps are suspended at a height of 5 m above the center of the floor.
- Each lamp emits 200 candlepower (cp) in all directions below the horizontal.
We can follow these steps to calculate the illumination:
Step 1: Calculate the intensity of each lamp at the point of interest.
The intensity of each lamp decreases with distance. In this case, the point of interest is the point on the floor mid-way between the second and third lamps. Let's call this point P.
For each lamp, we can use the inverse square law to calculate its intensity at point P. The inverse square law states that the intensity of light decreases with the square of the distance.
The distance from each lamp to point P is calculated as follows:
- Distance from the second lamp to point P: 0.1 m (distance between the lamps) + 1.5 m (half the distance between the second lamp and point P) = 1.6 m
- Distance from the third lamp to point P: 0.1 m (distance between the lamps) + 1.5 m (half the distance between the second lamp and point P) + 0.1 m (distance between the third lamp and the second lamp) = 1.8 m
Now, let's calculate the intensity of light at point P for each lamp using the inverse square law:
For the second lamp:
Intensity at point P = (200 cp) / (1.6 m)^2
For the third lamp:
Intensity at point P = (200 cp) / (1.8 m)^2
Step 2: Calculate the total illumination at point P by summing up the intensities of all lamps.
Since the lamps are independent sources of light, we can add up their intensities to get the total illumination at point P.
Total illumination at point P = Intensity from the second lamp + Intensity from the third lamp
Step 3: Calculate the final answer in terms of candlepower (cp).
The total illumination will give us the answer in candlepower (cp). This represents the combined brightness of all lamps at point P.
Illumination at the point on the floor mid-way between the second and third lamps = Total illumination at point P
By following these steps and calculating the intensities, you can find the illumination at the desired point on the floor.